Abstract:

The training of future mathematics teachers is an important challenge for Higher Education Institutions. We understand that we should be concerned with some difficulties that arise for these future teachers when some mathematical topics are taught during their academic course. If we can overcome these difficulties, we will contribute to the formation of excellent teachers with a richer scientific background and ready to face any obstacle in the exercise of their profession.
This communication was based on an investigation whose main objective was to know the performance of future Mathematics teachers of the 1st and 2nd Cycles of Portuguese Basic Education regarding the topic of “problem solving”.
Regarding the methodology, we have opted for a qualitative approach, with a case study design, by the use of a questionnaire survey and an evaluation test as a data collection instruments. The sample has consisted of 22 students: 17 of the female gender (77.3%) and five of the male gender (22.7%), aged between 17 and 19 years old, except in three cases, where the ages were 20, 22 and 29. The questionnaire was implemented in the 1st class of the curricular unit "Logic and Problem Solving" inserted in the 1st year, 1st semester, of the study plan of the 1st Cycle in Basic Education of a Portuguese university, in the academic year 2016/17. The questionnaire consisted of two parts: the first part was related with the students' personal identification data (gender, age, study area and their "relation" to Mathematics) and the second part consisted of five open questions about problem solving, and two mathematical problems that students would have to solve.
This work was focused on the resolutions presented by the future teachers to the two problems present in the questionnaire.
This study had indicated, in general, a poor performance of the future teachers regarding problem solving. In addition, as expected, the students from the area of Science and Technology of Portuguese Secondary Education, have demonstrated a greater aptitude and a better performance in problem solving when we compare with other students coming from other scientific areas.
The results obtained were not very exciting, identifying possible weaknesses in the knowledge of the future Mathematics teachers. Since these students will be future Mathematics teachers of the 1st and 2nd Cycles in Basic Education, it is important that we, as trainers of higher education of mathematical educators, be aware of this reality and start to give special attention to the difficulty in the topic "solving problem", so that the initial formation can overcome these deficiencies in a timely manner.

Keywords:

Problem solving, Initial teacher training, Basic Education.